This paper introduces a novel distributionally robust mean-variance portfolio estimator based on the projection robust Wasserstein (PRW) distance. This approach addresses the issue of increasing conservatism of portfolio allocation strategies due to high-dimensional data. Our simulation results show the robustness of the PRW-based estimator in the presence of noisy data and its ability to achieve a higher Sharpe ratio than regular Wasserstein distances when dealing with a large number of assets. Our empirical study also demonstrates that the proposed portfolio estimator outperforms classic “plug-in” methods using various covariance estimators in terms of risk when evaluated out of sample.

This paper proposes a novel robustness framework for studying the unit elasticity of intertemporal substitution (EIS) assumption based on the Perron-Frobenius sieve estimation model by Christensen, 2017. The sieve nonparametric decomposition is a central model that connects key strands of the long run risk literature and recovers the stochastic discount factor (SDF) under the unit EIS assumption. I generate various economies based on Epstein–Zin preferences to simulate scenarios where the EIS deviates from unity. Then, I study the main estimation mechanism of the decomposition as well as the time discount factor and the risk aversion parameter estimation surface. The results demonstrate the robustness of estimating the average yield, change of measure, and preference parameters but also reveal an “absorption effect” arising from the unit EIS assumption. The findings highlight that asset pricing models assuming a unit EIS produce distorted parameter estimates, caution researchers about the potential under- or over-estimation of risk aversion, and provide insight into trends of misestimation when interpreting the results. I also identify an additional source of failure from a consumption component, which demonstrates a more general limit of the consumption-based capital asset pricing model and the structure used to estimate relevant preference parameters.